From http://www.school-for-champions.com/science/fluidpressure.htm and http://www.school-forchampions.com/science/fluidfloating.htm by Ron Kurtus, School for Champions Pressure in Fluids by Ron Kurtus (revised 28 September 2002) Pressure is a measurement of the force per unit area. Since a fluid is a liquid or a gas, its pressure applies in all directions. Fluid pressure can be in an enclosed container or due to gravity or motion. The pressure can also be amplified through hydraulic mechanisms and changes with the velocity of the fluid. Questions you may have about pressure in fluids are: How does gravity cause fluid pressure? How does air and water pressure apply in all directions? What are other applications of fluid pressure? Fluid pressure from gravity or motion The weight of a fluid can exert a pressure on anything underneath it. Also, the relative movement of a liquid or gas can apply a pressure. Pressure Pressure (P) is defined as force (F) divided by the area (A) on which the force is pushing. (See the lesson on Pressure for details.) You can write this as an equation, if you wanted to make some calculations: P = F / A An object can exert downward pressure due to its weight and the force of gravity. The pressure you exert on the floor is your weight divided by the area of the soles of your shoes. If the force is due to the weight (W) of the object, the equation is then: Water pressure P = W / A The water pressure at the bottom of a lake is equal to the weight of the column of water above divided by the area of that column. Column on top of head If you were standing on the bottom of a swimming pool (assuming you would not start floating), there would be a column of water the diameter of your head all the way up to the water surface, pushing down on you. If you took that column of water and weighed it, and then divided that weight by the area of the top of your head, you would get the value for the water pressure. 1
Demonstration with can A demonstration of how water pressure increases with the depth of the water can be done with a large tin can. Punch nail holes in a vertical line up the side of the can every inch or several centimeters. Then fill the can with water. The water may just dribble out the top holes, but the increased pressure with depth causes the water to squirt out with more pressure at the bottom holes. Air pressure Likewise, the air pressure on the top of your head is the weight of the column of air (which is several miles high) divided by the area of the top of your head. The average air pressure on your head is 16 pounds per square inch! That is a lot of weight you are holding up. Air pressure in weather When weather report indicates high pressure, that means the column of air reaches up higher than it does for a low pressure reader. A barometer measures the air pressure or the weight of the column of air. Air pressure is due to the weight of all the air going several miles up above you. It is approximately 16 pounds per square inch in all directions on your body. Fortunately, our bodies have internal pressure that equalizes the air pressure. Balloons The air pressure inside a balloon pushes outward in all directions. When the pressure increases, the size of the balloon increases, until it finally bursts. The internal air pressure is much greater than the external air pressure. Different altitudes The normal air pressure in Denver, Colorado is less than in This is because the higher altitude of Denver means its column of air is not as high as in Milwaukee. Since many snacks are sealed in pressurized bags, a bag sealed in Milwaukee requires higher internal pressure than one made in Denver. Thus a Milwaukee bag of snacks will expand when brought to the lower air pressure of Denver and could even explode. Direction of fluid pressure Now, what is different about pressure caused by a liquid, or gas is that not only is there pressure pushing down at a given point, but there is also the same pressure pushing up and to the sides. All directions The pressure is the same in all directions in a fluid at a given point. This is true because of the characteristic of liquids and gases to take the shape of their container. 2
What this also means that any hollow container submersed in a liquid has pressure on every square inch of its surface, top and bottom. Swimming under water When you swim under water, the pressure of the water gets greater on your body, the deeper you get. Now, the question is: "Why aren't you crushed by all this weight?" The reason is that your body compensates by creating an internal pressure that is equal to the air or water pressure. You are somewhat like a balloon filled with fluids under pressure. Now, when you go very deep under water, the water pressure may get greater than your body can compensate for, and you get uncomfortable. Other pressure effects Other effects of fluid pressure are motion, heating and chemical effects, as well as applications in the field of hydraulics and in aircraft. (See Applications of Fluid Principles for details.) Wind and current The movement of a fluid, such as with wind or the current of a river can apply a pressure to an object in its way proportional to the surface area perpendicular to the direction of motion. Streamlining the object reduces this pressure. Heating and chemical effects When you heat a fluid, it usually expands. If you heat a fluid that is in an enclosed container, the expansion will result in greater internal pressure. For example, heating a balloon will cause it to expand. Likewise, chemical reactions that give off gases will increase the pressure inside the container. For example, shaking a carbonated drink bottle releases more gas and will result in greater internal pressure. This can be experienced when you open the bottle and the drink squirts all over. Hydraulics When a fluid--especially a liquid--is in a partially closed container, a force applied in one area can result in a greater force in another area. This effect is used in hydraulics to create a mechanical advantage by having the force applied to a small piston resulting in a greater force applied to large piston. Aircraft The scientist Bernoulli discovered that the air pressure in a tube goes down when the velocity of the air in the tube increases. This discovery became known as Bernoulli's Principle. The greatest application of this principle is used in airplanes. The wing of an airplane is usually curved on top and flat on the bottom. When the air moves over the curved top portion of the wing, it speeds up 3
because of the shape. This lowers the pressure with respect to the bottom part of the wing. Lower pressure on the top results in the lift required to keep the airplane aloft. In conclusion Fluid pressure from gravity is the weight of the fluid above divided by the area it is pushing on. Fluid pressure applies in all directions. Internal pressure of an object equals the external fluid pressure, otherwise the object could be crushed. Wind and heating can also create pressure. How Objects Float in Fluids by Ron Kurtus (revised 13 March 2003) When a solid object is placed in a fluid such as a liquid or gas, there is a buoyant force pushing the object upward. When that force is greater than the downward force of gravity, the object will float to the top of the fluid. Otherwise it will sink or remain in place in the fluid. Archimedes' Principle states that the buoyant force of a body is equal to the weight of the displaced liquid. Density = m/v Density*g = W/V If the density is greater than water, then the object will sink, but its apparent weight in water is its actual weight minus its bouyancy. Note on liquid floating. Floating means that an object or material will rise to the top of a fluid, despite the effect of gravity on the object. The force pushing the object upward is called the There are a number of factors related to whether an object will float or sink in a fluid. Objects placed in a fluid displace their volume of the fluid. If the density of the object is less than the density of the fluid, the object will float. Density is also related to specific gravity of the object. The weight of the object in a fluid is less than its weight outside the fluid. Questions you may have about floating are: What is displacement? What is density and specific gravity? How do things float? This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Useful tools: Metric-English Conversion Scientific Calculator. 4
Displacement Pressure is the same in all directions "Container" of water has equal up and down pressures 5
Gravity pulls denser object down Less dense object is pushed upward 6
Pressure equilibrium when floating Metal ship density less than water When a solid object is placed in a fluid, it displaces its volume in the fluid. In other words, it takes the place of a volume of the fluid equal to its own volume. For example, if you placed 1 cubic meter (1 m 3 ) object in a full container of water, 1 cubic meter of water would flow over the sides of the container. Of course, if you put the object in a container that won't overflow, the level of the fluid will rise, according to the added volume. The displacement principle is a factor in why certain objects float. It is also handy in being able to find the volume of irregularly shaped objects. 7
The volume or amount of space an object takes up is related to its density. Density and specific gravity The density of a material is how closely packed its matter is and is represented as its mass per unit volume. Specific gravity is a comparison of the density of a material with that of water. Density Density of a material is a combination of the atomic weight of its atoms and how tightly packed the atoms or molecules are. Different natural densities Different elements and materials have different natural densities. Water is denser than machine oil. Oxygen is denser than Helium. Although 100 pounds of feathers may take up much more room than 100 pounds of steel, they both still weigh 100 pounds. The steel is heavier for its size, due to the fact that it is a denser material. Comparison of the density of a solid with the density of a fluid will determine if the object will float in the fluid. Measuring density The density (d) of a material is its mass (m) divided by its volume (V). The equation for density is: d = m / V. Thus, a material such as feathers takes up much more room (volume) than a denser material such as steel, for the same mass or weight. The density of water in the metric system is 1 by the definition of the units: 1 cubic centimeter of water weighs 1 gram. Thus Density same on the Moon d = m/v = 1 gram / 1 cc = 1.0. Since density is related to the mass of an object, the density of a given volume of lead would be the same on both the Earth and the Moon, although the lead would weigh less on the Moon because of the lower gravity there. In English system In the English system of measurement, a pound is really a unit of weight on Earth and not mass. But we can still use pounds to get an idea of density. 8
Used to determine materials If you know the natural density of a pure element, and you know the weight and volume of an object, you can calculate its density and thus determine if it is a pure element. Specific Gravity Specific gravity is often used instead of density when comparing materials with water. The ratio of the density of an object compared with the density of water is defined as the material's specific gravity. Specific gravity is often used to compare liquids mixed with water. It is used in medicine. It is also used to determine the amount of acid in your car battery. Floating If you pushed a piece of wood under the water, a force will pull it up to the top surface, where it will float. Likewise, when you hold a balloon filled with Helium, you can feel a force pulling the balloon upward. The force that pushes an immersed object upward is a result of the fluid pressure from gravity and the difference in densities of the object and fluid. Fluid pressure from gravity At any depth in a fluid, the pressure in all directions is proportional to that depth. Thus, the water pressure at 10 meters is twice the pressure at 5 meters. An object under the water will have a downward pressure on its top proportional to the depth of its top, and it will have an upward pressure on its bottom, proportional to the depth of the bottom. Object sinks If an object weighed more than an equal volume of fluid--in other words, its density was greater, then the downward pressure at its bottom would be the weight of the fluid above plus the weight of the object. This force would be more than the upward force, due to only the weight of the water. Since the downward force is greater than the upward force, the object would sink. Concrete block in water An example would be a concrete block dropped in the water. The block's density or specific gravity is greater than that of the water, so the pressure at the bottom of the block from its weight would be greater than the upward pressure of the water at the point, and it would sink. Object floats 9
If the object weighed less than the fluid it displaces and was submerged in the fluid, the upward pressure would be greater than the downward pull of gravity and it would float. Wood floats Wood is less dense than water. When it is placed in water, the water it displaces equals its weight but not its volume. Thus the heavier water is pulled to the bottom by gravity, pushing the wood to the top. When an object floats in a fluid, the weight of the fluid displaced equals the weight of the object. In other words, the weight of the water a wooden block that floats one-half above the water surface equals the weigh of the block. If you add a weight to the top of the block, an equal weight of water will be displaced. Why ships float Boats or ships made of steel are hollow. The total weight is less than the water it displaces, and thus the ship will float. Different liquids can have different densities. For example, since a pint cooking oil is lighter in weight than the same volume of water, it is less dense than the water. Different gases can also have different densities. For example, helium is lighter than air, because it is less dense. A ship will displace a volume of water that is equal to the weight of the ship. That is why a loaded cargo ship will sit lower in the water than an unloaded one. The difference would be equal to the weight of the load. When liquids and gases are buoyant When you add liquids of different densities, the higher density liquid would tend to settle at the bottom of the container. The denser liquid exerts more pressure due to gravity, thus pushing the lighter material out of its way. That is why oil will float on the top of water and why air bubbles also float up to the top in water. An interesting observation is that bubbles starting at the bottom of a lake get bigger as the get closer to the surface. The reason is that the water pressure is less as they go up. This would also be true for a balloon full of air placed at different depths in water. Just as a balloon full of air is much less dense than the water it displaces, and the weight or pressure of the water pushes the balloon upward to the top of the water, a balloon full of Helium is lighter than its volume of air and thus is pushed upward into the atmosphere. Weighing object in fluid If you put an object that did not float in a fluid and weighed that object when it was submerged in that fluid, it would weigh its weight in air minus the weight of the fluid that it displaced. (In reality, you should weigh it in a vacuum, but the difference from weighing it in air is negligible.) 10
In other words, if you put a brick in a bucket of water that was filled to the brim and weighed the brick in the water, the measured weight would equal the weight of the brick in air minus the weight of the water that overflowed from the bucket. In conclusion Submerged objects displace their volume in the fluid. The density of an object is its mass per unit volume. Objects float when their density is less than the fluid. It is because the downward pressure of the object's weight is less than the upward pressure of the fluid at that depth. 11